Theoretical Interpretations and Applications of Radial Basis Function Networks

Medical applications usually used Radial Basis Function Networks just as Artificial Neural Networks. However, RBFNs are Knowledge-Based Networks that can be interpreted in several way: Artificial Neural Networks, Regularization Networks, Support Vector Machines, Wavelet Networks, Fuzzy Controllers, Kernel Estimators, Instanced-Based Learners. A survey of their interpretations and of their corresponding learning algorithms is provided as well as a brief survey on dynamic learning algorithms. RBFNs' interpretations can suggest applications that are particularly interesting in medical domains

Neural networks in geophysical applications

Neural networks are increasingly popular in geophysics. Because they are universal approximators, these tools can approximate any continuous function with an arbitrary precision. Hence, they may yield important contributions to finding solutions to a variety of geophysical applications. However, knowledge of many methods and techniques recently developed to increase the performance and to facilitate the use of neural networks does not seem to be widespread in the geophysical community. Therefore, the power of these tools has not yet been explored to their full extent. In this paper, techniques are described for faster training, better overall performance, i.e., generalization,and the automatic estimation of network size and architecture

Neural Network Methods for Boundary Value Problems Defined in Arbitrarily Shaped Domains

Partial differential equations (PDEs) with Dirichlet boundary conditions defined on boundaries with simple geometry have been succesfuly treated using sigmoidal multilayer perceptrons in previous works. This article deals with the case of complex boundary geometry, where the boundary is determined by a number of points that belong to it and are closely located, so as to offer a reasonable representation. Two networks are employed: a multilayer perceptron and a radial basis function network. The later is used to account for the satisfaction of the boundary conditions. The method has been successfuly tested on two-dimensional and three-dimensional PDEs and has yielded accurate solutions

Fast Selection of Spectral Variables with B-Spline Compression

The large number of spectral variables in most data sets encountered in spectral chemometrics often renders the prediction of a dependent variable uneasy. The number of variables hopefully can be reduced, by using either projection techniques or selection methods; the latter allow for the interpretation of the selected variables. Since the optimal approach of testing all possible subsets of variables with the prediction model is intractable, an incremental selection approach using a nonparametric statistics is a good option, as it avoids the computationally intensive use of the model itself. It has two drawbacks however: the number of groups of variables to test is still huge, and colinearities can make the results unstable. To overcome these limitations, this paper presents a method to select groups of spectral variables. It consists in a forward-backward procedure applied to the coefficients of a B-Spline representation of the spectra. The criterion used in the forward-backward procedure is the mutual information, allowing to find nonlinear dependencies between variables, on the contrary of the generally used correlation. The spline representation is used to get interpretability of the results, as groups of consecutive spectral variables will be selected. The experiments conducted on NIR spectra from fescue grass and diesel fuels show that the method provides clearly identified groups of selected variables, making interpretation easy, while keeping a low computational load. The prediction performances obtained using the selected coefficients are higher than those obtained by the same method applied directly to the original variables and similar to those obtained using traditional models, although using significantly less spectral variables

Why and When Can Deep -- but Not Shallow -- Networks Avoid the Curse of Dimensionality: a Review

The paper characterizes classes of functions for which deep learning can be exponentially better than shallow learning. Deep convolutional networks are a special case of these conditions, though weight sharing is not the main reason for their exponential advantage